My front gears can move up just fine, but to go from 3 to 2 I have to go 3 all the way down to 1 then up to 2 for the chain to engage. Doesn't even seem to try on 3 to 2.
This is often caused by either too much friction in the derailleur cables or the derailleur being sticky because they weren't lubricated. The derailleur is trying to pull itself down from 3 to 2 but isn't strong enough until you change to 1, which is when there's enough tension to bring it all the way down to 1.
You have to either reduce the friction in the spring or in the cable.
Clean your derailleur with a degreaser and relube with a good oil.
Then try to lubricate your cables (unless you have teflon inner cables, which are only found on more expensive / newer bikes) with a dry graphite or teflon lube.
If that doesn't work, I'd replace your front derailleur cables. The cable housing and inner is about 10-15 eurodollars and you might be able to do it yourself. The only special tools you need are hex wrenches, Allen keys, or a screwdriver for the derailleur, cable cutter for the inner derailleur cable, and neednose pliers to crimp the cable ferrule.
Or you can ask your shop to do it. Should be only 0.5 hours labor.